Paper connects contrastive learning to MI maximization and establishes robust methods for nonlinear ICA and subspace estimation.
problem Understanding and improving unsupervised representation learning and density ratio estimation.
method The paper connects contrastive learning to MI maximization, establishes new recovery conditions for nonlinear ICA, and proposes a practical outlier-robust method for nonlinear subspace estimation.
result The proposed methods can be seen as maximizing MI, performing nonlinear ICA, or estimating nonlinear subspaces, and are robust to outliers.
Letter analyzes training dynamics of a nonlinear contrastive learning model in high dimensions.
problem Understanding training dynamics of nonlinear contrastive learning models in high-dimensional settings.
method High-dimensional analysis using McKean-Vlasov PDEs and low-dimensional ODEs.
result The model's performance evolves according to specific ODEs, revealing features like feature learnability and noise effects.
Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable. Here, we first propose a new intuitive principle of unsupervised deep learning from time series which uses the nonstationary structure of the data. Our l…
FactorGCL uses hypergraph learning to predict stock returns by mining hidden factors.
problem Mining effective factors in data-driven models is challenging due to low signal-to-noise ratio in market data.
method FactorGCL employs a hypergraph structure and temporal residual contrastive learning to extract hidden factors.
result FactorGCL outperforms existing methods and mines effective hidden factors for predicting stock returns.
This work closes the gap between theory and practice for nICA identifiability.
problem Identifying latent components in nonlinearly mixed data.
method Finite-sample analysis of GCL-based nICA, combining GCL properties, statistical generalization, and numerical differentiation.
result Establishes a trade-off between function learner complexity and expressiveness.
This paper presents SimCLR: a simple framework for contrastive learning of visual representations. We simplify recently proposed contrastive self-supervised learning algorithms without requiring specialized architectures or a memory bank. In order to understand what enables the contrastive prediction tasks to learn use…
Paper investigates multimodal contrastive learning and incorporates unpaired data.
problem Improving feature learning ability of multimodal models under noisy data.
method Initiates investigation of nonlinear loss functions for multimodal contrastive learning, analyzes performance, proposes new loss incorporating unpaired data.
result MMCL can outperform unimodal contrastive learning and robustly handle noisy data.
Unified framework for self-supervised learning via latent distribution matching.
problem Lack of a unifying theoretical framework for diverse SSL methods.
method Casting SSL as latent distribution matching (LDM): maximizing alignment and uniformity.
result Derives a Bayesian filtering model and proves identifiable latent representations.
We consider the problem of learning a forest of nonlinear decision rules with general loss functions. The standard methods employ boosted decision trees such as Adaboost for exponential loss and Friedman's gradient boosting for general loss. In contrast to these traditional boosting algorithms that treat a tree learner…
Nonlinear ICA is a fundamental problem for unsupervised representation learning, emphasizing the capacity to recover the underlying latent variables generating the data (i.e., identifiability). Recently, the very first identifiability proofs for nonlinear ICA have been proposed, leveraging the temporal structure of the…
We learn linear models from nonlinear systems using multiple trajectories and regularization.
problem Identifying linear models from data when the underlying dynamics are nonlinear.
method Multiple trajectories data acquisition followed by regularized least squares.
result Learn linearized dynamics with arbitrarily small error given enough samples.
New method identifies causal relationships from interventions in complex systems.
problem Learning causal representations from unknown, latent interventions with general nonlinear mixing.
method Strong identifiability results with unknown single-node interventions, using geometric structure of transformed data.
result First instance of causal identifiability from non-paired interventions for deep neural network embeddings.
Machine Learning improves macroeconomic forecasting by capturing nonlinearities.
problem Improving macroeconomic forecasting accuracy.
method Study four features (nonlinearities, regularization, cross-validation, loss function) in data-rich and data-poor environments.
result Nonlinearity is the key to improving forecasting accuracy.
Nonlinear independent component analysis (ICA) is a general framework for unsupervised representation learning, and aimed at recovering the latent variables in data. Recent practical methods perform nonlinear ICA by solving a series of classification problems based on logistic regression. However, it is well-known that…
We identify linear models from nonlinear systems with initialization constraints.
problem Identifying linear models from nonlinear systems with initialization constraints.
method Multiple trajectories-based deterministic data acquisition algorithm followed by regularized least squares.
result We provide a finite sample error bound on the learned linearized dynamics.
This paper tackles sequential distribution shifts in representation learning.
problem Learning meaningful representations in a sequence of distribution shifts.
method Nonlinear Independent Component Analysis (ICA) framework for continual causal representation learning.
result The method achieves performance comparable to joint training on multiple offline distributions and shows no benefit from the incoming new distribution on all latent variables.
Classification and regression in which the inputs are graphs of arbitrary size and shape have been paid attention in various fields such as computational chemistry and bioinformatics. Subgraph indicators are often used as the most fundamental features, but the number of possible subgraph patterns are intractably large …
Novel method learns time series dynamics without reconstruction.
problem Learning nonlinear stochastic dynamics from video data.
method Recognition-parametrized Gaussian state space model (RP-GSSM) using maximum likelihood.
result Outperforms alternatives on nonlinear stochastic dynamics learning.
We propose a Fourier-based learning algorithm for highly nonlinear multiclass classification. The algorithm is based on a smoothing technique to calculate the probability distribution of all classes. To obtain the probability distribution, the density distribution of each class is smoothed by a low-pass filter separate…
New method removes contrastive loss by adding a prediction head, revealing learning mechanisms.
problem Understanding why neural networks learn competitive representations despite trivial optima.
method Empirical and theoretical analysis of a trainable, identity-initialized prediction head.
result The trainable prediction head enables learning all features, preventing dimensional collapse.
New methods improve feature extraction and representation quality in supervised and unsupervised DR.
problem Statistical dependence, data diversity, contrast, and interpretability in conventional DR methods.
method Combines linear and nonlinear formulations for three new independence criteria.
result Significant improvements in contrast, accuracy, and interpretability over baselines.
Neural networks learn to mimic brain neurons with two-input activation functions, improving performance and robustness.
problem Training neural networks to mimic the complex interactions of brain neurons.
method Developed a network-in-network architecture with two-input activation functions, optimized hyperparameters, and compared to conventional ReLU networks.
result Two-input activation functions can learn soft XOR functions, improving network performance and robustness.
New RL approach tackles non-linear MDPs without linear assumptions.
problem Sample efficiency in RL for complex, nonlinear MDPs with continuous states.
method Introduces EPW condition to relax linear structure requirements; provides sample-efficient RL algorithm.
result EPW condition allows solving MDPs without linear assumptions, including Atari games.
Learning nonlinear dynamics from aggregate data is a challenging problem because the full trajectory of each individual is not available, namely, the individual observed at one time may not be observed at the next time point, or the identity of individual is unavailable. This is in sharp contrast to learning dynamics w…
While most classical approaches to Granger causality detection assume linear dynamics, many interactions in real-world applications, like neuroscience and genomics, are inherently nonlinear. In these cases, using linear models may lead to inconsistent estimation of Granger causal interactions. We propose a class of non…
Bayesian neural networks improve macroeconomic forecasting and model nonlinearities.
problem Handling small T, big K macroeconomic datasets with temporal dependence.
method Developed Bayesian neural networks with mixture activation functions, shrinkage priors, and stochastic volatility.
result BNNs produce precise density forecasts, often better than other methods.
Novel neural operator predicts complex spatiotemporal dynamics from partial observations.
problem Capturing complex operator dynamics in infinite-dimensional function spaces.
method Integrates Koopman operator theory with deep neural networks to approximate nonlinear operators between Banach spaces.
result BNO achieves robust zero-shot super-resolution in unsteady flow prediction and outperforms conventional methods.
Proposes a new Q-learning method for survival outcomes in clinical trials.
problem Incomplete follow-up data and nonlinear covariate effects in clinical trials.
method Combines Buckley-James boosting with flexible base learners for estimating optimal treatment regimes.
result Improves treatment decision accuracy and stability in longitudinal clinical trials.
TTT improves model adaptation to test data, especially for nonlinear models.
problem Improving model performance in adapting to test data, especially for nonlinear models.
method Combining Test-time Training (TTT) with In-context Learning (ICL) for nonlinear models.
result TTT enables models to adapt to both feature vector and link function shifts, improving performance.
ADA augments data using AR replicas for robust regression.
problem Improving robustness in nonlinear over-parametrized regression.
method Extends Anchor regression (AR) for data augmentation, using replicas of modified samples.
result ADA provides more robust regression predictions compared to state-of-the-art solutions.
In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mil…
A new model approximates complex functions in parameter space.
problem Complex and nonlinear functional regression problems.
method Mapping-to-Parameter function model with B-spline free knot placement.
result Robust knot placement algorithms improve model performance.
Paper proposes a DNN-driven AF framework for improved generalization.
problem Generalization challenge in adaptive filtering.
method Structural embedding of DNN into AF system, using maximum likelihood as implicit cost function.
result Demonstrates improved generalization capability through extensive experiments.
DCMA uses generative models to analyze treatment effects on entire outcome distributions.
problem Traditional mediation analysis focuses on summary contrasts, missing complex distributional changes.
method DCMA learns conditional generative models for mediators and outcome, reconstructing interventional distributions via Monte Carlo simulation.
result DCMA captures both summary effects and rich distributional contrasts like energy distance and Wasserstein distance.
DCMA uses generative models to analyze complex treatment effects on outcome distributions.
problem Analyzing complex and nonlinear causal mechanisms through outcome-level summary contrasts.
method Generative learning framework for identifying and estimating treatment effects on entire outcome distributions.
result Reconstructs interventional outcome distributions via Monte Carlo forward simulation, capturing both summary and distributional contrasts.
This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of t…
Convexity preserved in curved surfaces moving at concave speeds.
problem Deforming convex surfaces with concave speeds.
method Nonlinear geometric flows with concave speed functions.
result High curvature regions remain approximately convex.
In this paper, we propose a new variational model for image reconstruction by minimizing the L1 norm of the \emph{Weingarten map} of image surface (x,y,f(x,y)) for a given image f:Ω→R. We analytically prove that the Weingarten map minimization model can not only keep the greyscale int…
Quantum machine learning solves high-dimensional PDEs with lower variance and improved accuracy.
problem Approximating solutions to high-dimensional parabolic PDEs.
method Pure Variational Quantum Circuit (VQC) for BSDE approximation, using temporal discretization and Monte Carlo simulation.
result VQC achieves lower variance and improved accuracy in most cases, particularly in highly nonlinear regimes.
We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider t…
A novel feature selection method for SVM improves model accuracy and interpretability.
problem Feature selection in nonlinear SVM classification problems.
method Embedded min-max optimization problem, leveraging duality theory.
result Improves model accuracy and interpretability on benchmark data sets.
We develop a new DTSM with nonlinearities using Gaussian Processes for better interest rate forecasting.
problem Linear DTSMs fail to capture nonlinear relationships between macroeconomic variables and interest rates.
method We propose a Gaussian Process-based sequential Monte Carlo estimation and forecasting scheme.
result Nonlinear models outperform linear ones in forecasting core inflation, leading to significant economic value gains.
We propose a method for maximizing a partial area under a receiver operating characteristic (ROC) curve (pAUC) for binary classification tasks. In binary classification tasks, accuracy is the most commonly used as a measure of classifier performance. In some applications such as anomaly detection and diagnostic testing…
A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometri…
In this paper we propose solving localized multiple kernel learning (LMKL) using LMKL-Net, a feedforward deep neural network. In contrast to previous works, as a learning principle we propose {\em parameterizing} both the gating function for learning kernel combination weights and the multiclass classifier in LMKL usin…
Transformers learn low-dimensional target functions efficiently in-context.
problem Efficiently learning nonlinear target functions in-context using transformers.
method Nonlinear MLP layer in transformers optimized by gradient descent, focusing on single-index target functions.
result Transformers can learn target functions with low-dimensional structures efficiently in-context.
A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.
problem Ill-conditioning in Dirac-Frenkel residual minimization leads to non-unique parameter dynamics.
method Introduces a history variable (momentum) to select better-conditioned parameter velocities, preserving residual minimization while promoting smooth parameter evolutions.
result The approach leads to increased robustness in singular and near-singular PDE solution regimes.
This paper tackles data-efficient nonlinear control in Hamiltonian systems using symplectic geometry.
problem Data-efficient nonlinear control in Hamiltonian systems.
method Combines symplectic geometry, recurrence on energy level sets, and chain policies to solve target reachability problems.
result Data requirements depend on geometric and recurrence properties of the Hamiltonian, not the state dimension.